# Mean in Cumulative frequencies distribution

Monthly expense     Cumulative Freq.
up to 50            7
up to 80            25
up to 120           49
up to 200           58
over  200           60


Calculate the arithmetic mean knowing that the 2 families with the higher expense, spend together 500.

So I started calculating Absolute Frequencies and Middle values of the classes (doing 500 / 2 as max value for the last class):

Absolute freq.      Middlevalues    Absolute freq. * Middlevalues
7               25              175
18              65              1170
24              100             2400
9               160             1440
2               225             450
=   60                              = 5635


Arithmetic mean = 5635 / 60 = 93,91666667

But it's wrong because the sum of residuals is not zero (Middlevalues-Mean):

-68,91666667
-28,91666667
6,083333333
66,08333333
131,0833333
= 105,4166667


What am I doing wrong?

• (1) The middle value of the largest class, of $225$, is inconsistent with the assertion that the total of this class is $500$. (2) You have not summed the residuals correctly because you did not account for their varying frequencies. There should be $60$ residuals in your sum, not $5$ of them. – whuber Sep 26 '14 at 17:31
• (1) I don't get that. The latest class is 200-250 (since they spend together 500..).. So (200+250)/2=225. (2). Ok that's clear. – MultiformeIngegno Sep 27 '14 at 21:32
• There is no basis for assuming the last class ends at 250. – whuber Sep 28 '14 at 3:59
• Ok thanks. So the mean is not 93,91666667 but..? – MultiformeIngegno Sep 29 '14 at 9:54